Problem: Rewrite the expression in the form $k\cdot z^n$. $\left(27\sqrt[3]{z^2}\right)^{^{\scriptsize\dfrac13}}=$
Solution: $\begin{aligned} \left(27\sqrt[3]{z^2}\right)^{^{\scriptsize\dfrac13}}&=\left(27z^{^{\scriptsize\dfrac23}}\right)^{^{\scriptsize\dfrac13}} \\\\ &=27^{^{\scriptsize\dfrac13}} \cdot z^{^{\scriptsize\dfrac23\cdot\dfrac13}} \\\\ &=3z^{^{\scriptsize\dfrac29}} \end{aligned}$